Digital predistortion with out-of-band and peak expansion regularization

ABSTRACT

An apparatus that implements DPD in a manner that can address OOB instability issues, PE instability issues, or both, is disclosed. The apparatus includes an actuator circuit configured to use a model of a power amplifier (PA) to apply a predistortion to at least a portion of an input signal, and an error correction circuit configured to generate an error signal indicative of a deviation of the output of the actuator circuit from the target output, e.g., in terms of OOB or PE. The apparatus also includes an adaptation circuit configured to update the model based on the error signal. By using such an error in adapting the model used for the DPD, undesirable effects of performing DPD, such as creation or amplification of OOB frequency components, or increasing amplitude of some samples, may be reduced or eliminated.

RELATED APLICATIONS

This application claims the benefit of and priority from U.S. patentapplication Ser. No. 16/656,036 filed on Oct. 17, 2019, herebyincorporated by reference in its entirety.

TECHNICAL FIELD OF THE DISCLOSURE

The present disclosure generally relates to electronics, and, morespecifically, to predistorting input to circuits with nonlinearresponses.

BACKGROUND

Both, systems used for wireless communication such as Long TermEvolution (LTE) and 5^(th) generation (5G), and systems used for cablecommunication such as cable television networks, are radio systems inthat they transmit and receive signals in the form of electromagneticwaves in the radio frequency (RF) range of approximately 3 kilohertz(kHz) to 300 gigahertz (GHz). In both of these types of systems a poweramplifier that is used to amplify RF signals prior to transmission is acrucial component.

Power amplifiers can generate amplified RF signals that includenonlinear distortions. The response of power amplifiers with nonlineardistortions can result in reduced modulation accuracy (e.g., reducederror vector magnitude (EVM)) and/or out-of-band emissions. Accordingly,communication systems have stringent specifications on power amplifierlinearity.

Digital predistortion (DPD) can be applied to enhance linearity of apower amplifier. Typically, DPD involves applying, in the digitaldomain, predistortion to an input signal to be provided as an input to apower amplifier to reduce and/or cancel distortion that is expected tobe caused by the power amplifier. The predistortion can be characterizedby a power amplifier model. The power amplifier model can be updatedbased on the feedback from the power amplifier (i.e., based on theoutput of the power amplifier). The more accurate a power amplifiermodel is in terms of predicting the distortions that the power amplifierwill introduce, the more effective the predistortion of an input to thepower amplifier will be in terms of reducing the effects of thedistortion caused by the amplifier.

Obtaining an accurate power amplifier model that may be used to performDPD is not trivial and further improvements would be desirable.

BRIEF DESCRIPTION OF THE DRAWINGS

To provide a more complete understanding of the present disclosure andfeatures and advantages thereof, reference is made to the followingdescription, taken in conjunction with the accompanying figures, whereinlike reference numerals represent like parts, in which:

FIG. 1 illustrates a schematic block diagram of a communication systemwith a DPD circuit configured to implement OOB and/or PE regularization,according to some embodiments of the present disclosure;

FIG. 2 provides an illustration of an OOB instability;

FIG. 3 illustrates an example result of an OOB instability;

FIG. 4 illustrates a schematic block diagram of a portion of acommunication system with a DPD circuit that attempts to limit DPDbandwidth expansion;

FIG. 5 illustrates a schematic block diagram of a portion of acommunication system with a DPD circuit with OOB regularization,according to some embodiments of the present disclosure;

FIG. 6 illustrates a schematic block diagram of a portion of acommunication system with a DPD circuit with PE regularization,according to some embodiments of the present disclosure;

FIG. 7 illustrates example signals at various portions of a DPD circuitwith PE regularization, according to some embodiments of the presentdisclosure;

FIG. 8 provides a flow chart of a method for implementing DPD using anerror signal, according to some embodiments of the present disclosure;and

FIG. 9 provides a schematic block diagram of an example data processingsystem that may be configured to implement at least portions of DPD withOOB and/or PE regularization, according to some embodiments of thepresent disclosure.

DESCRIPTION OF EXAMPLE EMBODIMENTS OF THE DISCLOSURE Overview

The systems, methods and devices of this disclosure each have severalinnovative aspects, no single one of which is solely responsible for allof the desirable attributes disclosed herein. Details of one or moreimplementations of the subject matter described in this specificationare set forth in the description below and the accompanying drawings.

For purposes of illustrating DPD techniques proposed herein, it might beuseful to first understand phenomena that may come into play incommunication systems. The following foundational information may beviewed as a basis from which the present disclosure may be properlyexplained. Such information is offered for purposes of explanation onlyand, accordingly, should not be construed in any way to limit the broadscope of the present disclosure and its potential applications.

As described above, DPD can pre-distort an input to a power amplifier toreduce and/or cancel distortion caused by the amplifier. To realize thisfunctionality, at a high level, DPD involves forming a model of how apower amplifier may affect an input signal, the model definingcoefficients of a filter to be applied to the input signal in an attemptto reduce and/or cancel distortions of the input signal caused by theamplifier. In this manner, DPD will try to compensate for the amplifierapplying an undesirable nonlinear modification to the signal to betransmitted, by applying a corresponding modification to the inputsignal to be provided to the amplifier.

The model used in DPD algorithms is an adaptive model, meaning that itis formed in an iterative process by gradually adjusting thecoefficients based on the comparison between the data that comes in tothe input to the amplifier and the data that comes out from the outputof the amplifier. Estimation of DPD coefficients is based on acquisitionof finite sequences of input and output data (i.e., input to and outputfrom a power amplifier), commonly referred to as “captures,” andformation of a feedback loop in which the model is adapted based on theanalysis of the captures. More specifically, DPD algorithms are based onforming a set of equations commonly referred to as “update equations,”and searching for suitable solutions to the equations, in a broadsolution space, to update the model of the power amplifier. To that end,DPD algorithms solve an inverse problem, which is the process ofcalculating, from a set of observations, the casual factors thatproduced these observations. Solving inverse problems in the presence ofnonlinear effects is very challenging and may be ill-posed. Inparticular, inventors of the present disclosure realized that, undersome conditions, such as limited loop bandwidth and limited peak powerof a power amplifier, may be ill-posed by definition and possess nostable, workable solution in practice. If that happens, RF transmissionof signals may be compromised not only because of power amplifiersdistorting input signals provided thereto, but also because the DPDalgorithms themselves create undesirable artefacts in signals to betransmitted. At best, such artefacts may negatively affect linearity ofpower amplifiers. At worst, they may render the amplifiers inoperablealtogether.

One such artefacts is referred to in the present disclosure as“out-of-band (OOB) instability.” An input signal to be amplified by apower amplifier typically includes frequency components in a certaintarget band, such frequency components referred to as “in-bandcomponents.” However, if there is a band-limiting effect (e.g., if thereis a filtering effect where the applied signal frequency content ismodified, removed, or attenuated in some fashion) anywhere in a signalchain between a DPD actuator circuit and a power amplifier (e.g., a DACreconstructing filter may be low pass in nature), conventional DPDalgorithms often try to compensate for the effect by expanding the OOBfrequency components in an input signal to be provided to the poweramplifier. As a result, while an input signal provided to a DPD actuatorcircuit may, largely, only include the in-band frequency components,with no or very little energy in OOB components, an output of the DPDactuator circuit may have a non-negligible amount of energy in OOBfrequency components, in addition to the in-band components. Forexample, the output of the DPD actuator circuit may have a bandwidththat is K times as wide as its' input bandwidth, where K is the highestorder of the DPD correction used. The output of the DPD actuator circuitis eventually provided to the power amplifier, and an output of thepower amplifier is provided, as a feedback signal, to the DPD adaptationcircuit, which may be set on a wrong path of search for solutionsbecause of the presence of the OOB components, resulting inunstable/unbounded behavior of the DPD in terms of creation of OOBcomponents.

Another such artefact is referred to in the present disclosure as “peakexpansion (PE) instability.” Power amplifiers may have limited peakpower capabilities, meaning that their gain may collapse at somehigh-power peaks. To compensate for that behavior, conventional DPDsolutions may try to increase (i.e., expand) the peaks, which only makesthe matters worse by also setting the DPD adaptation circuit on a wrongpath in search of solutions and resulting in unstable/unbounded behaviorof the DPD in terms of PE.

As the foregoing illustrates, conventional DPD algorithms leave room forimprovement in terms of generating signals having OOB and/or PEinstability issues.

One aspect of the present disclosure provides an apparatus thatimplements DPD in a manner that can address OOB instability issues, PEinstability issues, or both. An example apparatus includes an actuatorcircuit configured to use a model of a nonlinear electronic component(e.g., a power amplifier) to apply a predistortion to at least a portionof an input signal to generate an output of the actuator circuit (i.e.,to predistort the input signal prior to providing it to the poweramplifier), and an error correction circuit configured to generate anerror signal (e.g., ε_(oob) or ε_(peak), described herein) indicative ofa deviation of the output of the actuator circuit from a target/desiredoutput. For example, the error signal may be indicative of the OOBfrequency components that may be present in the output of the actuatorcircuit, or the error signal may be indicative of peaks, in the outputof the actuator circuit, having an amplitude beyond a certain threshold.The apparatus also includes an adaptation circuit configured to updatethe model based on one or more captures of a feedback signal indicativeof (e.g., including, or being based on) an output of the power amplifier(where capture includes L consecutive samples of the feedback signal,where L is an integer equal to or greater than 2), and further based onthe error signal. By using such an error in adapting a model used toperform DPD, undesirable effects of applying DPD, such as creation oramplification of OOB frequency components, or increasing amplitude ofsome samples, may be reduced or eliminated. Consequently, DPD may bemore effective in reducing the distortions caused by the poweramplifier, thereby advantageously improving its linearity.

Using an error signal indicative of OOB frequency components that may bepresent in the output of a DPD actuator circuit may reduce or eliminatethe OOB instability of the DPD by diverting the DPD algorithm from thesolutions that result in creation of OOB frequency components.Therefore, DPD that adapts a power amplifier model based on such anerror signal is referred to herein as “DPD with OOB regularization”(since, in general, in mathematics and computer science, particularly inmachine learning and inverse problems, “regularization” refers to theprocess of adding information in order to solve an ill-posed problem orto prevent overfitting). Similarly, using an error signal indicative ofpeaks, in the output of the actuator circuit, having an amplitude beyonda certain threshold may reduce or eliminate the PE instability of theDPD by diverting the DPD algorithm from the solutions that result increation of such high-amplitude peaks. Therefore, DPD that adapts apower amplifier model based on such an error signal is referred toherein as “DPD with PE regularization.”

While some of the descriptions are provided herein with reference topower amplifiers, in general, various embodiments of the methods ofdigital predistortion with OOB and/or PE regularization presented hereinare applicable to any nonlinear electronic components (i.e., componentsthat may exhibit nonlinear behavior) other than power amplifiers.

As will be appreciated by one skilled in the art, aspects of the presentdisclosure, in particular aspects of DPD with OOB and/or PEregularization as described herein, may be embodied in variousmanners—e.g. as a method, a system, a computer program product, or acomputer-readable storage medium. Accordingly, aspects of the presentdisclosure may take the form of an entirely hardware embodiment, anentirely software embodiment (including firmware, resident software,micro-code, etc.) or an embodiment combining software and hardwareaspects that may all generally be referred to herein as a “circuit,”“module” or “system.” Functions described in this disclosure may beimplemented as an algorithm executed by one or more hardware processingunits, e.g., one or more microprocessors, of one or more computers. Invarious embodiments, different steps and portions of the steps of anymethods described herein may be performed by different processing units.Furthermore, aspects of the present disclosure may take the form of acomputer program product embodied in one or more computer-readablemedium(s), preferably non-transitory, having computer-readable programcode embodied, e.g., stored, thereon. In various embodiments, such acomputer program may, for example, be downloaded (updated) to theexisting devices and systems (e.g. to the existing RF transmitters,receivers, and/or their controllers, etc.) or be stored uponmanufacturing of these devices and systems.

The following detailed description presents various descriptions ofspecific certain embodiments. However, the innovations described hereincan be embodied in a multitude of different ways, for example, asdefined and covered by the claims or select examples. In the followingdescription, reference is made to the drawings where like referencenumerals can indicate identical or functionally similar elements. Itwill be understood that elements illustrated in the drawings are notnecessarily drawn to scale. Moreover, it will be understood that certainembodiments can include more elements than illustrated in a drawingand/or a subset of the elements illustrated in a drawing. Further, someembodiments can incorporate any suitable combination of features fromtwo or more drawings.

The description may use the phrases “in an embodiment” or “inembodiments,” which may each refer to one or more of the same ordifferent embodiments. Unless otherwise specified, the use of theordinal adjectives “first,” “second,” and “third,” etc., to describe acommon object, merely indicate that different instances of like objectsare being referred to, and are not intended to imply that the objects sodescribed must be in a given sequence, either temporally, spatially, inranking or in any other manner. Various aspects of the illustrativeembodiments are described using terms commonly employed by those skilledin the art to convey the substance of their work to others skilled inthe art. The terms “substantially,” “approximately,” “about,” etc., maybe used to generally refer to being within +/−20% of a target valuebased on the context of a particular value as described herein or asknown in the art. For the purposes of the present disclosure, the phrase“A and/or B” or notation “A/B” means (A), (B), or (A and B). For thepurposes of the present disclosure, the phrase “A, B, and/or C” means(A), (B), (C), (A and B), (A and C), (B and C), or (A, B, and C). Theterm “between,” when used with reference to measurement ranges, isinclusive of the ends of the measurement ranges. As used herein, thenotation “A/B/C” means (A, B, and/or C).

Example Communication System with DPD with OOB and PE Regularization

As summarized above, some embodiments of the present disclosure relateto performing DPD with OOB and/or PE regularization. To that end, asystem as shown in FIG. 1 may be used.

FIG. 1 illustrates a schematic block diagram of a communication system100 with a DPD circuit 110 configured to implement OOB and/or PEregularization, according to some embodiments of the present disclosure.FIG. 1 illustrates that the communication system 100 may include atransmitter circuit (or, simply, a “transmitter”) 120 in communicationwith the DPD circuit 110, and a power amplifier 130 in communicationwith the transmitter 120. At least a portion of the output from thepower amplifier may be provided, as a feedback signal, to a receivercircuit (or, simply, a “receiver”) 140 that is also in communicationwith the DPD circuit 110.

As shown in FIG. 1, the DPD circuit 110 may include a DPD actuator 112,configured to apply predistortion (or, more generally, modification) toan input signal provided to the DPD actuator. The DPD circuit 110 mayalso include a coefficient generator circuit 170 configured to generatecoefficients to be used by the DPD actuator 112 to apply thepredistortion. The coefficient generator circuit 170 may include anadaptation circuit 172, and one or both of an OOB regularization circuit174 and a PE regularization circuit 176. The receiver 120 may include adigital filter 122, a digital-to-analog converter (DAC) 124, an analogfilter 126, and a mixer 128. The transmitter 140 may include a digitalfilter 142, an analog-to-digital converter (ADC) 144, an analog filter146, and a mixer 148. In various embodiments, the communications system100 can include fewer or more elements than those illustrated in FIG. 1.

As shown in FIG. 1, an input signal x (which may be a sequence ofdigital samples and which may be a vector) may be received by the DPDactuator 112. In some embodiments, the input signal x may include one ormore active channels in the frequency domain, but, for simplicity, aninput signal with only one channel (i.e., a single frequency range ofin-band frequencies) is described. In some embodiments, the input signalx may be a baseband digital signal. The DPD actuator 112 may beconfigured to predistort the input signal x based on predistortioncoefficients provided by the coefficient generator circuit 170, therebygenerating an output signal v, as shown in FIG. 1 (as used herein, lowercase, bold italics single-letter labels used in the present figures,such as e.g., v, or x, shown in FIG. 1, refer to a vector). In turn, thecoefficient generator circuit 170, e.g., the adaptation circuit 172 ofthe coefficient generator circuit 170, may be configured to generate thepredistortion coefficients based on a model that uses an error signalindicative of OOB frequency components that may be present in the outputof the DPD actuator 112 and/or an error signal indicative of peaks, inthe output of the DPD actuator 112, having an amplitude beyond a certainthreshold, described in greater detail below. The former error signalmay be generated by the OOB regularization circuit 174 and may bereferred to as an “OOB error signal,” while the latter error signal maybe generated by the PE regularization circuit 176 and may be referred toas a “PE error signal.” The DPD actuator 112 can provide thepredistorted input v (which may be a sequence of digital samples of theoutput signal from the DPD actuator 112), which is the input signal x towhich predistortion has been applied, to the transmitter 120. The DPDactuator 112 can be implemented by any suitable circuits. For instance,in some embodiments, the DPD actuator 112 can be implemented bycombinational logic circuits.

The transmitter 120 may be configured to upconvert the predistortedinput v from a baseband signal to a higher frequency signal, such as anRF signal. In the illustrated transmitter 120, the predistorted input vmay be filtered in the digital domain by the digital filter 122 togenerate a filtered predistorted input, a digital signal. The output ofthe digital filter 122 may then be converted to an analog signal by theDAC 124. The analog signal provided by the DAC 124 may then be filteredby an analog filter 126. The output of the analog filter 126 may then beupconverted to RF by the mixer 128, which may receive a signal from alocal oscillator 150 to translate the filtered analog signal from theanalog filter 126 from baseband to RF. Other methods of implementing thetransmitter 120 are also possible and within the scope of the presentdisclosure. For instance, in another implementation (not illustrated)the output of the digital filter 122 can be directly converted to an RFsignal by the DAC 124. In such an implementation, the RF signal providedby the DAC 124 can then be filtered by the analog filter 126. Since theDAC 124 would directly synthesize the RF signal in this implementation,the mixer 128 and the local oscillator 150 illustrated in FIG. 1 can beomitted from the system 100 in such embodiments.

As further illustrated in FIG. 1, the RF signal generated by thetransmitter 120 is provided to the power amplifier 130. The poweramplifier 130 amplifies the RF signal and provides an amplified RFsignal z (which may be a vector). The amplified RF signal z can beprovided to an antenna (not illustrated in FIG. 1) to be wirelesslytransmitted. The amplified RF signal z has a signal bandwidth. Thesignal bandwidth can be a wide bandwidth. As one non-limiting example,the signal bandwidth can be about 1 GHz. Ideally, the amplified RFsignal z should just be an amplified version of the input signal x.However, as discussed above, the amplified RF signal z can havedistortions outside of the main signal components. Such distortions canresult from nonlinearities in the response of the power amplifier 130.As discussed above, it can be desirable to reduce such nonlinearities.Accordingly, feedback from the output of the power amplifier 130 can beprovided to the DPD circuit 110 by way of the receiver 140. Then the DPDcircuit 110 can cause the predistortion applied to the input signal x tobe adjusted.

To provide feedback to the DPD circuit 110, a portion 131 of theamplified RF signal z can be provided to the receiver 140. For example,in some embodiments, a feedback element (not illustrated) may be used inthe signal path between the output of the power amplifier 130 and thereceiver 140, e.g., a resistive element that feeds back a relativelysmall portion of the amplified RF signal to the receiver 140. In someother embodiments (also not illustrated), a directional coupler or othersuitable circuit can provide a portion of the amplified RF signal z tothe receiver 140. In some embodiments (not illustrated), a feedbackfilter may be provided in the signal path between the output of thepower amplifier 130 and the receiver 140, e.g., to filter the feedbacksignal 131 and provide the filtered signal as a feedback signal to thereceiver 140 for processing. The feedback signal 131 provided to thereceiver 140 can have approximately the same bandwidth as the amplifiedRF signal z.

In some embodiments, the receiver 140 is configured to performdiagnostics and/or equalization. Accordingly, the receiver 140 can beutilized for providing feedback to the DPD circuit 110 and fordiagnostics and/or equalization in such embodiments. In the illustratedreceiver 140, the feedback signal 131 may be downconverted to thebaseband by the mixer 148, which may receive a signal from a localoscillator 160 (which may be the same or different from the localoscillator 150) to translate the feedback signal 131 from the RF to thebaseband. The output of the mixer 148 may then be filtered by the analogfilter 146. The output of the analog filter 146 may then be converted toa digital signal by the ADC 144. The digital signal generated by the ADC124 may then be filtered in the digital domain by the digital filter 142to generate a filtered downconverted feedback signal 141 which may beprovided to the DPD circuit 110. FIG. 1 labels the feedback signal 141provided to the DPD circuit 110 as a signal y (which may be a sequenceof digital values indicative of the output z of the power amplifier 130,and which may also be modeled as a vector). Other methods ofimplementing the receiver 140 are also possible and within the scope ofthe present disclosure. For instance, in another implementation (notillustrated) the RF feedback signal 131 can be directly converted to abaseband signal by the ADC 144. In such an implementation, thedownconverted signal provided by the ADC 144 can then be filtered by thedigital filter 142. Since the ADC 144 would directly synthesize thebaseband signal in this implementation, the mixer 148 and the localoscillator 160 illustrated in FIG. 1 can be omitted from the system 100in such embodiments.

Further variations are possible to the system 100, described above. Forexample, while upconversion and downconversion is described with respectto the baseband frequency, in other embodiments of the system 100, anintermediate frequency (IF) may be used instead. IF may be used insuperheterodyne radio receivers, in which a received RF signal isshifted to an IF, before the final detection of the information in thereceived signal is done. Conversion to an IF may be useful for severalreasons. For example, when several stages of filters are used, they canall be set to a fixed frequency, which makes them easier to build and totune. In some embodiments, the mixers of RF transmitter 120 or thereceiver 140 may include several such stages of IF conversion. Inanother example, although a single path mixer is shown in each of thetransmit (TX) path (i.e., the signal path for the signal to be processedby the transmitter 120) and the receive (RX) path (i.e., the signal pathfor the signal to be processed by the receiver 140) of FIG. 1, in someembodiments, the TX path mixer 128 and the RX path mixer 148 may beimplemented as a quadrature upconverter and downconverter, respectively,in which case each of them would include a first mixer and a secondmixer. For example, for the RX path mixer 148, the first RX path mixermay be configured for performing downconversion to generate an in-phase(I) downconverted RX signal by mixing the feedback signal 131 and anin-phase component of the local oscillator signal provided by the localoscillator 160. The second RX path mixer may be configured forperforming downconversion to generate a quadrature (Q) downconverted RXsignal by mixing the feedback signal 131 and a quadrature component ofthe local oscillator signal provided by the local oscillator 160 (thequadrature component is a component that is offset, in phase, from thein-phase component of the local oscillator signal by 80 degrees). Theoutput of the first RX path mixer may be provided to a I-signal path,and the output of the second RX path mixer may be provided to a Q-signalpath, which may be substantially 80 degrees out of phase with theI-signal path.

Functionality of the OOB regularization circuit 174 and the PEregularization circuit 176 will be described in the following sections.Again, in some embodiments, the DPD circuit 110 may include only the OOBregularization circuit 174 but not the PE regularization circuit 176; inother embodiments, the DPD circuit 110 may include only the PEregularization circuit 176 but not the OOB regularization circuit 174;and, still in other embodiments, DPD circuit 110 may include both theOOB regularization circuit 174 and the PE regularization circuit 176.

OOB Regularization

Turning to the details of the DPD circuit 110, functionality ofperforming DPD with OOB regularization according to various embodimentsof the present disclosure may be illustrated with reference to FIGS.2-6.

FIG. 2 provides an illustration of an OOB instability that may becreated as a result of applying conventional DPD by a DPD actuator 212.As shown in FIG. 2, an input signal to the DPD actuator 212 may be asignal 202 having a certain band of frequency components, i.e., thein-band components. However, at the output of the DPD actuator may be asignal that contains not only the in-band components 202, but also thirdorder nonlinear terms 204 and fifth order nonlinear terms 206.Furthermore, if there is a band-limiting effect anywhere in the signalpath of the signal 202, conventional DPD will try to compensate byexpanding the OOB components 208, resulting in unstable and/or unboundedsolution.

FIG. 3 shows a graph 300 that illustrates an example result of an OOBinstability. The horizontal axis of the graph 300 is used to measure thenumber of iterations of a DPD algorithm (i.e., the number of times themodel coefficients are adapted). The vertical axis of the graph 300 isused to measure DPD peak expansion, which may be computed as a ratio ofthe peak at the output of a DPD actuator to the peak at the input to theDPD actuator. For example, the vertical axis of the graph 300 may beused to measure a ratio of the peak at the output signal v of the DPDactuator 212, which output signal includes components 202, 204, 206, and208, as described above, to the peak at the input signal to the DPDactuator 212, which input signal includes substantially only the in-bandcomponents 202. A curve 302 shown in FIG. 3 illustrates that, at thebeginning (e.g., the first few iterations), the peak expansion is about0 dB, prior to any DPD training. However, as the system adapts, due tothe band limiting effect, the DPD expands to values of 6-8 dB, over 2and ½ times the input peak amplitude. All the individual blocks aroundthe loop have a finite operating range and only a limited expansion canbe supported in practice. If any of the blocks around the loop haveinsufficient headroom to support this level of expansion, then they willhard clip (e.g., saturate) and compound the distortion from the poweramplifier (e.g., the DAC, the upconverter, pre-amp stages, etc., maybegin to compress and then hard clip). With growing levels ofcompression, the DPD reacts with further expansion, and a positivefeedback cycle of deepening compression followed by widening DPDexpansion emerges, which can lead to the eventual and dramatic loss ofperformance.

Some conventional DPD solutions have attempted to limit DPD bandwidthexpansion, one of them shown in FIG. 4. FIG. 4 illustrates a schematicblock diagram of a portion of a communication system 400 with a DPDcircuit that attempts to limit DPD bandwidth expansion. In particular,FIG. 4 illustrates a DPD actuator 412 and some portions of thetransmitter signal chain following the DPD actuator 412, such as a DAC424, an analog filter 426, a mixer 428, and a power amplifier 430 (whichcould be analogous to the DAC 124, the analog filter 126, the mixer 128,and the power amplifier 130, described above). Details of the DPDactuator 412 are also shown in FIG. 4. An input signal, e.g., the inputsignal 202 as described above, may be provided to the DPD actuator 412where it is processed by different DPD kernels 414 (K of which are shownin FIG. 4 but, in order to not clutter the drawing, only one of which islabeled in FIG. 4 with a reference numeral 414-1, indicating that it's afirst instance of a DPD kernel 414). Each DPD kernel 414 is followed bya filter 416 (again, K of which are shown in FIG. 4 but, in order to notclutter the drawing, only one of which is labeled in FIG. 4 with areference numeral 416-1, indicating that it's a first instance of afilter 416), which is typically an LPF, in order to filter out the OOBcomponents which may be created by the respective DPD kernels 414. TheDPD kernels 414-1 to 414-K are configured generate the memoryless terms;order 1 (linear), order 2, . . . up to order K. Each of these terms areexpanded in bandwidth by their respective order (e.g., order K term isexpanded by K times). They are followed by respective 416-1 to 416-K,which are filters that limit the bandwidth (e.g., to the lowestbandwidth around the loop). The filters 416 are followed by respective418-1 to 418-K, which are adaptive filters whose coefficients{circumflex over (θ)} are trained during the DPD training. In thesolution of FIG. 4, 414 and 418 are components of a conventional DPD.The outputs of 418 are then added by an adder 420 to generate an outputof the DPD actuator 412.

What is new in this solution is 416, which is added to solve the OOBinstability problem. As shown with a schematic of a signal on the rightside of FIG. 4, such implementation of the DPD actuator 412 may helpreducing peak expansion in that components 404 added to the in-bandsignal 202 as smaller than those shown in the illustration of FIG. 2.However, implementing different band-limited kernels, in particular,implementing multiple instances of the filters 416 as additionalhardware components, is very expensive, both in terms of cost and powerconsumption (i.e., the solution of FIG. 4 comes at a substantial cost asthe solution now requires K additional filters costing gates and power).As such, the implementation shown in FIG. 4 is not an option for someimplementations, such as cable communication systems.

FIG. 5 illustrates a schematic block diagram of a portion 500 of thecommunication system 100 shown in FIG. 1, with a DPD circuit with OOBregularization, according to some embodiments of the present disclosure.FIG. 5 illustrates some elements with the same reference numerals asthose used in FIG. 1 to indicate that these elements are the same oranalogous as those described with reference to FIG. 1 so that, in theinterests of brevity, their description is not repeated. In particular,FIG. 5 illustrates the DPD actuator 112, the DAC 124, the poweramplifier 130, and the ADC 144. Other components of the transmitter 120and the receiver 140 which were shown in FIG. 1 are not shown in FIG. 5in order to not clutter the drawing because the illustration of FIG. 5focuses on the example implementation of the adaptation circuit 172(approximate functional boundaries of which are shown in FIG. 5 with adash-dotted contour) and of the OOB regularization circuit 174(approximate functional boundaries of which are shown in FIG. 5 with adashed contour).

As shown in FIG. 5, the adaptation circuit 172 may include an adaptivepostdistortion circuit 502, an adder/subtractor 504, and an adaptationcircuit 506. As in conventional adaptive loops used to perform DPD, thefeedback signal 141 (also labeled as a signal y in FIG. 5, as in FIG. 1)is received by the adaptive postdistortion circuit 502, which may thengenerate a postdistorted signal 503 by applying model coefficients{circumflex over (θ)} (a vector) to the feedback signal 141, and thepostdistorted signal 503 is then provided to the adder/subtractor 504.The postdistorted signal 503 is labeled in FIG. 5 with a hat symbol({circumflex over (v)}) to indicate that it's an approximation or anestimate of the output 513 of the DPD actuator circuit 112.

The adder/subtractor 504 is configured to also receive the output 513(also labeled as a signal ν in FIG. 5, as in FIG. 1) of the DPD actuatorcircuit 112. The output 513 is generated by the DPD actuator circuit 112by applying model coefficients {circumflex over (θ)} to the input signal511, shown in FIG. 5. The adder/subtractor 504 is configured to generatea DPD error signal 505 (ε_(dpd), shown in FIG. 5) indicative of adifference between the output 513 of the actuator circuit 112 (i.e., asignal which may not only include the in-band frequency components butalso the OOB frequency components) and the postdistorted feedback signal503 indicative of the output of the power amplifier 130, as providedfrom the adaptive postdistortion circuit 502. The DPD error signalε_(dpd) is then provided to the adaptation circuit 506 which may updatethe model of the power amplifier 130 (i.e., update the coefficients tobe applied by the DPD actuator 112 in a subsequent iteration) based onthe DPD error signal 505 (ε_(dpd)) and provide updated coefficients{circumflex over (θ)} both to the adaptive postdistortion circuit 502,as shown in FIG. 5 with a communication path labeled as 507-1, and tothe DPD actuator circuit 112, as shown in FIG. 5 with a communicationpath labeled as 507-2 (the hat symbols provided above the coefficients θnear the paths 507-1 and 507-2 indicate that the coefficients{circumflex over (θ)} are an estimate or an approximation).

Importantly, the adaptation circuit 506 is configured to update themodel of the power amplifier 130 not only based on the DPD error signal505 (ε_(dpd)) but also based on an OOB error signal 509 (ε_(oob), alsoshown in FIG. 5). To that end, the OOB regularization circuit 174 may beimplemented as shown in FIG. 5, where the OOB regularization circuit 174may include a filter 508, configured to receive the output 513 of theactuator circuit 112 and to use the received output 513 to generate theOOB error signal 509 which is indicative of the OOB (i.e., undesired)frequency components that might be present in the output 513 of theactuator circuit 112. For example, in some embodiments, the filter 508may be a high-pass filter configured to attenuate (e.g., reduce oreliminate) the in-band frequency components from the output 513 whilesubstantially passing the OOB frequency components that may be presentin the output 513. In some other embodiments, the filter 508 mayattenuate (i.e., decrease in amplitude) or amplify (i.e., increase inamplitude) the OOB frequency components by a relatively small amount.For example, while it might be preferable in some embodiments toimplement the filter 508 so that it would simply pass the OOB componentsto the output 509, without any attenuation or amplification to thesecomponents (i.e., the factor by which the amplitude of these componentsis adjusted is substantially 1.0), in some other embodiments the filter508 may amplify the OOB components. For example, the factor by which theamplitude of these components is adjusted from the input to the filter508 (i.e., the signal 513) to the output of the filter 508 (i.e., thesignal 509) may be between about 1.0 and 2.0, including all values andranges therein, e.g., between about 1.0 and 1.5, or between about 1.0.and 1.2. In other embodiments, the filter 508 may be attenuate the OOBcomponents, e.g., with the factor by which the amplitude of thesecomponents is adjusted being between about 0.5 and 1.0, including allvalues and ranges therein, e.g., between about 0.7 and 1.0, or betweenabout 0.9 and 1.0. If any attenuation is applied by the filter 508 tothe OOB components, this would be very different to the attenuationfactor applied by the filter 508 to attenuate the in-band components,where the attenuation factor for the in-band components may be betweenabout 0 and 0.5, or between 0 and 0.2, so that the in-band componentsare attenuated more than the out-of-band components.

Other implementations of the OOB regularization circuit 174 may be usedand are within the scope of the present disclosure as long as the OOBerror signal 509 generated by the OOB regularization circuit 174 is suchthat the greater the OOB components in the output 513 of the DPDactuator circuit 112, the larger is the OOB error signal 509. The OOBerror signal 509 may then be used by the adaptation circuit 506, inaddition to the DPD error signal 505, to update the model and generateupdated coefficients {circumflex over (θ)} to be provided to theadaptive postdistortion circuit 502 and to the DPD actuator circuit 112,to be used in subsequent iterations.

In some embodiments, the adaptation of the system 500 may function asfollows. The model of the power amplifier 130 may include a loss term,or function, that is a multi-objective loss that includes a first termand a second term. The first term may be indicative of a differencebetween the feedback signal 141 and the output 513 of the DPD actuatorcircuit 112. The second term may be indicative of an amount and/or amagnitude of the OOB frequency components present in the output 513 ofthe actuator circuit 112, thus providing a measure of the DPD output 513that falls out of band, such as the power or mean square value. Forexample, the first term may be indicative of (e.g., be based on) the DPDerror signal 505, while the second term may be indicative of the OOBerror signal 509. At least one of the first term and the second term maybe a mean squared value. For example, the loss function may be amulti-objective loss function defined as:

(ε_(dpd), ε_(oob))=E{ε _(dpd) ²}+λ_(oob) E{ε _(oob) ²},   (1)where the first term, E{ε_(dpd) ²}, may be indicative of the LeastSquares (OLS) DPD loss (where “ordinary” is understood as meaning noregularization is used), and may be based on the mean squared value ofthe DPD error signal 505 (ε_(dpd)), while the second term, E{ε_(oob) ²},may be indicative of the OOB loss, and may be based on the mean squaredvalue of the OOB error signal 509 (ε_(oob)). In this equation, parameterλ_(oob) may be a weight that defined how heavily the OOB error signal isto be weighed in the loss function. In this way, by incorporating thesecond term into the loss function, the adaptation circuit 506 may beconfigured to penalize DPD solutions having OOB content, where thegreater is the weight λ_(oob), the heavier the penalty may be. Theadaptation circuit 506 may then be configured to update the model basedon the DPD error signal 505 and the OOB error signal 509 with the goalof decreasing the loss function.

In some embodiments, the adaptation circuit 506 updating the model basedon the OOB error signal 509 to decrease the loss function may includethe adaptation circuit implementing a Gauss-Newton algorithm to decreasethe loss function, although, in other embodiments, other algorithms maybe used.

In some embodiments, the coefficients may be updated according to thefollowing update equation:{circumflex over (θ)}_(k)={circumflex over (θ)}_(k−1) +μ{Y ^(H) Y+λ_(oob) U ^(H) U} ⁻¹ {Y ^(H)ε_(dpd)+λ_(oob) U ^(H)ε_(oob)},   (2)

-   -   where Y is the negative gradient, (Jacobian) of E{ε_(dpd) ²}), U        is the negative gradient, (Jacobian) of E{ε_(oob) ²},        U=−X⊗h_(oob), X DPD basis matrix whose column vectors are the        DPD features, h_(oob) is a band stop filter over the band of        interest (e.g., stops in-band, passes OOB frequency components),        and X⊗h_(oob) is the convolution of the column vectors of X with        h_(oob).

When DPD output 513 (i.e., v) contains only in-band content OOB error,ε_(oob) and gradient u are both 0 and the DPD is unpenalized.Conversely, when the DPD actuator 112 produces OOB content, penalizationand OOB regularization increases.

As the foregoing description illustrates, the adaptation circuit 506updating the model of the power amplifier 130 in the communicationsystem 100/500 includes the adaptation circuit 506 computing updatedfilter coefficients to be used in applying the predistortion by the DPDactuator circuit 112. Thus, the DPD circuit 110 is configured to updatefilter coefficients which are used in applying the DPD based on the OOBerror signal generated by the OOB regularization circuit 174, whicheffectively modifies the adaptation algorithm. In some embodiments, suchmodification to an adaptation may reside in software only, in contrastto some conventional solutions for decreasing OOB content describedabove, which rely on adding hardware in the form of LPFs at the outputof each DPD term of the DPD actuator to explicitly filter out the OOBcontent from the output of the DPD actuator. As described above, addingthese additional LPFs in conventional solutions is expensive both interms of gate count (i.e., more transistors have to be implemented,taking up valuable space) and power consumption. On the other hand, theDPD circuit 110 described herein may be realized with a much smallercost, compared to such conventional solutions, by implicitly shaping theDPD terms to have attenuation of OOB components by virtue ofappropriately updating the model coefficients.

PE Regularization

Continuing with further details of the DPD circuit 110, functionality ofperforming DPD with PE regularization according to various embodimentsof the present disclosure may be illustrated with reference to FIGS.6-7.

FIG. 6 illustrates a schematic block diagram of a portion 600 of thecommunication system 100 shown in FIG. 1, with a DPD circuit with PEregularization, according to some embodiments of the present disclosure.FIG. 6 illustrates some elements with the same reference numerals asthose used in FIG. 1 and FIG. 5 to indicate that these elements are thesame or analogous as those described with reference to FIG. 1 and FIG. 5so that, in the interests of brevity, their description is not repeated.In particular, FIG. 6 illustrates the DPD actuator 112, the DAC 124, thepower amplifier 130, and the ADC 144. Other components of thetransmitter 120 and the receiver 140 which were shown in FIG. 1 are notshown in FIG. 6 in order to not clutter the drawing because theillustration of FIG. 6 focuses on the example implementation of theadaptation circuit 172 (approximate functional boundaries of which areshown in FIG. 6 with a dash-dotted contour) and of the PE regularizationcircuit 176 (approximate functional boundaries of which are shown inFIG. 6 with a dashed contour). Furthermore, example implementation ofthe adaptation circuit 172 shown in FIG. 6 is the same as the one shownin FIG. 5 to indicate that the same adaptation circuit 172 may be usedto cooperate with the PE regularization circuit 176 of FIG. 6 as the onethat may be used to cooperate with the OOB regularization circuit 174 ofFIG. 5. In fact, in some embodiments, the DPD circuit 110 may includeboth the OOB regularization circuit 174 and the PE regularizationcircuit 176, as described above. Therefore, descriptions of theadaptation circuit 172 provided above are not repeated here and only thedifferences are described.

As shown in FIG. 6, the PE regularization circuit 176 may include meansfor generating an error signal 619 (ε_(peak), shown in FIG. 6), similarto the OOB error signal 509, described above, but now the error signal619 being indicative of samples in the output 513 of the DPD actuatorcircuit 112 which have amplitude greater than a certain threshold. Theadaptation circuit 506 may then be configured to update the model of thepower amplifier 130 based on the DPD error signal 505 (ε_(dpd)) as wellas based on the PE error signal 619 (ε_(peak)). The adaptation circuit506 may update the model by updating the coefficients to be applied bythe DPD actuator 112 in a subsequent iteration and may provide updatedcoefficients {circumflex over (θ)} both to the adaptive postdistortioncircuit 502 (as shown in FIG. 6 with the communication path 507-1) andto the DPD actuator circuit 112 (as shown in FIG. 6 with thecommunication path 507-2).

In some embodiments, the PE regularization circuit 176 may beimplemented as shown in FIG. 6, where the PE regularization circuit 176may include a clipping circuit 608 and an adder/subtractor 618. Theclipping circuit 608 may be configured to receive the output 513 of theactuator circuit 112 and to use the received output 513 to generate aclipped output signal 609 in which the amplitude of the samples in theoutput 513 of the actuator circuit 112 which have the amplitude greaterthan the threshold. The adder/subtractor 618 may then receive, both, theoutput 513 of the actuator circuit 112 and the clipped output 609, andgenerate the PE error signal 619, e.g., as a difference between theoutput 513 and an output 609 (i.e., the output of the actuator circuitin which the clipping circuit 608 clipped the amplitude of the samplesfor those samples that had the amplitude greater than the threshold).

FIG. 7 illustrates example signals at various portions of a DPD circuitwith PE regularization, e.g., of the DPD circuit 110 as shown in FIG. 6,according to some embodiments of the present disclosure. In particular,a curve 702 shown in FIG. 7 illustrates an example output of the DPDactuator 112, e.g., the output 513, described above. A curve 704 shownin FIG. 7 illustrates an example output of the clipping circuit thatclips amplitudes above a certain threshold, e.g., the output 609 of theclipping circuit 608, described above. A curve 706 shown in FIG. 7illustrates an example output of the PE regularization circuit 176,e.g., the output 619 (i.e., the PE error signal), described above.

Other implementations of the PE regularization circuit 176 may be usedand are within the scope of the present disclosure as long as the PEerror signal 619 generated by the PE regularization circuit 176 is suchthat the more samples of the output 513 exceed the threshold, and by thegreater amount, the larger is the power of the PE error signal 619. ThePE error signal 619 may then be used by the adaptation circuit 506, inaddition to the DPD error signal 505, to update the model and generateupdated coefficients e to be provided to the feedback predistortioncircuit 502 and to the DPD actuator circuit 112, to be used insubsequent iterations.

In some embodiments, the adaptation of the system 600 may function asfollows. The model of the power amplifier 130 may include a loss term,or function, that is a multi-objective loss that includes a first termand a second term. The first term may be as that described above withreference to the OOB regularization. The second term may be indicativeof how the output 513 of the actuator circuit 112 exceeds a certainthreshold. For example, the first term may be indicative of (e.g., bebased on) the DPD error signal 505, while the second term may beindicative of the PE error signal 619. At least one of the first termand the second term may be a mean squared value. For example, the lossfunction may be a multi-objective loss function defined as:

(ε_(dpd), ε_(peak))=E{ε _(dpd) ²}+λ_(peak) E{ε _(peak) ²},   (3)where the first term, E{ε_(dpd) ² }, may be indicative of the OLS DPDloss, and may be based on the mean squared value of the DPD error signal505 (ε_(dpd)), while the second term, E{ε_(peak) ²}, may be indicativeof the PE loss, and may be based on the mean squared value of the PEerror signal 619 (ε_(peak)). In this equation, parameter λ_(peak) may bea weight that defined how heavily the PE error signal is to be weighedin the loss function. In this way, by incorporating the second term intothe loss function, the adaptation circuit 506 may be configured topenalize DPD solutions having content with high peaks, where the greateris the weight λ_(peak), the heavier the penalty may be. The adaptationcircuit 506 may then be configured to update the model based on the DPDerror signal 505 and the PE error signal 619 with the goal of decreasingthe loss function.

In some embodiments, the adaptation circuit 506 updating the model basedon the PE error signal 619 to decrease the loss function may include theadaptation circuit implementing a Gauss-Newton algorithm to decrease theloss function, although, in other embodiments, other algorithms may beused.

In some embodiments, the coefficients may be updated based on the PEerror signal 619 according to the following update equation:{circumflex over (θ)}_(k)={circumflex over (θ)}_(k−1) +μ{Y ^(H) Y+λZ^(H) Z} ⁻¹ {Y ^(H)ε_(dpd) +λZ ^(H)ε_(peak)},   (4)where Y is the negative gradient, (Jacobian) of E{ε_(dpd) ²}), Z is thenegative gradient, (Jacobian) of

${E\left\{ ɛ_{peak}^{2} \right\}},{Z = {X - {X\frac{\partial z}{\partial v}}}},$X DPD basis matrix.

When the input to the DPD actuator, x, is within the saturation limits,peak and gradient Z are going towards 0 and the solver is not penalized.Conversely, when the DPD actuator 112 produces high peaks, penalizationand PE regularization increases to direct the adaptation circuit 506towards another solution.

Example DPD Method Based on Generating an Error Signal

DPD with OOB and/or PE regularization as described above may be extendedto a general approach of including a circuit, e.g., within the DPDcircuit 110, e.g., within the coefficient generation circuit 170, thatis configured to receive the output of the DPD actuator 112 and generatean error signal that would be indicative of any kind ofundesired/offensive behavior in the output signal. The error signal maybe such that the greater the undesired/offensive behavior, in terms ofone or more suitable metrics, the larger the signal is (e.g., the largerthe mean square value of the error signal is). Such an error signal maythen be used by the adaptation circuit 172 to update the model andgenerate updated coefficients for one or more of the subsequentiterations.

FIG. 8 provides a flow chart of a method 800 for implementing DPD usingsuch an error signal, e.g., for implementing DPD with OOB and/or PEregularization as described above, according to some embodiments of thepresent disclosure. At least portions of the method 800 may beimplemented by elements of a communication system according to anyembodiments of the present disclosure, e.g., by the communication systemdescribed with reference to FIGS. 1, 5, and/or 6, and/or by one or moredata processing systems, such as the data processing system 900 shown inFIG. 9. Although described with reference to system components of thesystems shown in the present figures, any system, configured to performoperations of the method 800, in any order, is within the scope of thepresent disclosure. Furthermore, it should be noted that, while adifferentiation is made, both in the illustration of the communicationsystems shown in FIGS. 1, 5, and 6, and in the illustration of themethod 800 shown in FIG. 8, between a regularization circuit and anadaptation circuit, this differentiation may be only functional/logical,to merely differentiate functions that may be performed by aconventional DPD circuit and functions specifically related to DPD withOOB and/or PE regularization. In various embodiments, functionality ofany of the regularization circuits described herein, e.g., the OOBregularization circuit 174, the PE regularization circuit 176, or anygeneral regularization circuit, may be included, or be considered as apart of the adaptation circuit 172, or functionalities of these twocircuits may be spread over a larger number of individual circuits.

The method 800 may begin with an operation 802 that includes the DPDactuator circuit 112 receiving an input signal, e.g., the signal 511,described above. In operation 804, the DPD actuator circuit 112 may usea model of the power amplifier 130 to apply predistortion to the inputsignal received in 802 to generate a predistorted output signal, e.g.,the signal 513, described above. The method 800 may then proceed to anoperation 806 that includes a regularization circuit receiving thepredistorted output signal from the DPD actuator circuit 112 andgenerating an error signal based on the received signal. For example,806 may include the OOB regularization circuit 174 generating the OOBerror signal as described above, the PE regularization circuit 176generating the PE error signal as described above, or any generalregularization circuit generating an error signal indicative of somekind of offensive behavior other than generation of the OOB componentsor PE. The method 800 may further include an operation 808 in which theadaptation circuit 172 (e.g., the adaptation circuit 506, describedabove) uses the error signal generated in 806 to update the model andgenerate updated filter coefficients to be applied by the DPD actuatorcircuit 112 in one or more subsequent iterations of the method 800. Tothat end, 808 may include the adaptation circuit 172 updating the modelnot only based on the error signal generated in 806, but also using aDPD error signal that may be generated based on comparing a feedbacksignal indicative of the output of the power amplifier 130 and thepredistorted output generated by the DPD circuit 112. In someembodiments, 808 may include the adaptation circuit 172generating/evaluating a loss function in terms of the error signalgenerated in 806 and the DPD error signal and update the model in anattempt to minimize the loss function, as described above for theexamples of the loss functions for OOB regularization and PEregularization. The method 800 may then proceed with the next iteration,now with the updated model coefficients, as shown in FIG. 8 with anarrow from 808 to 802.

Example Data Processing System

FIG. 9 provides a schematic block diagram of an example data processingsystem 900 that may be configured to implement at least portions of DPDwith OOB and/or PE regularization, or DPD using any error signalaccording to the method 800, according to some embodiments of thepresent disclosure. For example, the data processing system 900 may beused to implement at least portions of the communication system asdescribed with reference to FIGS. 1, 5, and 6, in particular, toimplement at least portions of the DPD circuit 110 as described herein.

As shown in FIG. 9, the data processing system 900 may include at leastone processor 902, e.g. a hardware processor 902, coupled to memoryelements 904 through a system bus 906. As such, the data processingsystem may store program code within memory elements 904. Further, theprocessor 902 may execute the program code accessed from the memoryelements 904 via a system bus 906. In one aspect, the data processingsystem may be implemented as a computer that is suitable for storingand/or executing program code. It should be appreciated, however, thatthe data processing system 900 may be implemented in the form of anysystem including a processor and a memory that is capable of performingthe functions described within this disclosure.

In some embodiments, the processor 902 can execute software or analgorithm to perform the activities as discussed in this specification,in particular activities related to DPD with OOB and/or PEregularization, or DPD using any error signal according to the method800, such as various techniques implemented by the DPD circuit 110described herein. The processor 902 may include any combination ofhardware, software, or firmware providing programmable logic, includingby way of non-limiting example a microprocessor, a DSP, afield-programmable gate array (FPGA), a programmable logic array (PLA),an integrated circuit (IC), an application specific IC (ASIC), or avirtual machine processor. The processor 902 may be communicativelycoupled to the memory element 904, for example in a direct-memory access(DMA) configuration, so that the processor 902 may read from or write tothe memory elements 904.

In general, the memory elements 904 may include any suitable volatile ornon-volatile memory technology, including double data rate (DDR) randomaccess memory (RAM), synchronous RAM (SRAM), dynamic RAM (DRAM), flash,read-only memory (ROM), optical media, virtual memory regions, magneticor tape memory, or any other suitable technology. Unless specifiedotherwise, any of the memory elements discussed herein should beconstrued as being encompassed within the broad term “memory.” Theinformation being measured, processed, tracked or sent to or from any ofthe components of the data processing system 900 could be provided inany database, register, control list, cache, or storage structure, allof which can be referenced at any suitable timeframe. Any such storageoptions may be included within the broad term “memory” as used herein.Similarly, any of the potential processing elements, modules, andmachines described herein should be construed as being encompassedwithin the broad term “processor.” Each of the elements shown in thepresent figures, e.g., any of the circuits/components shown in FIGS. 1,5, and 6, can also include suitable interfaces for receiving,transmitting, and/or otherwise communicating data or information in anetwork environment so that they can communicate with, e.g., the dataprocessing system 900 of another one of these elements.

In certain example implementations, mechanisms for implementing DPD withOOB and/or PE regularization, or DPD using any error signal according tothe method 800, in communication systems as outlined herein may beimplemented by logic encoded in one or more tangible media, which may beinclusive of non-transitory media, e.g., embedded logic provided in anASIC, in DSP instructions, software (potentially inclusive of objectcode and source code) to be executed by a processor, or other similarmachine, etc. In some of these instances, memory elements, such as e.g.the memory elements 904 shown in FIG. 9, can store data or informationused for the operations described herein. This includes the memoryelements being able to store software, logic, code, or processorinstructions that are executed to carry out the activities describedherein. A processor can execute any type of instructions associated withthe data or information to achieve the operations detailed herein. Inone example, the processors, such as e.g. the processor 902 shown inFIG. 9, could transform an element or an article (e.g., data) from onestate or thing to another state or thing. In another example, theactivities outlined herein may be implemented with fixed logic orprogrammable logic (e.g., software/computer instructions executed by aprocessor) and the elements identified herein could be some type of aprogrammable processor, programmable digital logic (e.g., an FPGA, aDSP, an erasable programmable read-only memory (EPROM), an electricallyerasable programmable read-only memory (EEPROM)) or an ASIC thatincludes digital logic, software, code, electronic instructions, or anysuitable combination thereof.

The memory elements 904 may include one or more physical memory devicessuch as, for example, local memory 908 and one or more bulk storagedevices 910. The local memory may refer to RAM or other non-persistentmemory device(s) generally used during actual execution of the programcode. A bulk storage device may be implemented as a hard drive or otherpersistent data storage device. The processing system 900 may alsoinclude one or more cache memories (not shown) that provide temporarystorage of at least some program code in order to reduce the number oftimes program code must be retrieved from the bulk storage device 910during execution.

As shown in FIG. 9, the memory elements 904 may store an application918. In various embodiments, the application 918 may be stored in thelocal memory 908, the one or more bulk storage devices 910, or apartfrom the local memory and the bulk storage devices. It should beappreciated that the data processing system 900 may further execute anoperating system (not shown in FIG. 9) that can facilitate execution ofthe application 918. The application 918, being implemented in the formof executable program code, can be executed by the data processingsystem 900, e.g., by the processor 902. Responsive to executing theapplication, the data processing system 900 may be configured to performone or more operations or method steps described herein.

Input/output (I/O) devices depicted as an input device 912 and an outputdevice 914, optionally, can be coupled to the data processing system.Examples of input devices may include, but are not limited to, akeyboard, a pointing device such as a mouse, or the like. Examples ofoutput devices may include, but are not limited to, a monitor or adisplay, speakers, or the like. In some embodiments, the output device914 may be any type of screen display, such as plasma display, liquidcrystal display (LCD), organic light emitting diode (OLED) display,electroluminescent (EL) display, or any other indicator, such as a dial,barometer, or light emitting diode (LED). In some implementations, thesystem may include a driver (not shown) for the output device 914. Inputand/or output devices 912, 914 may be coupled to the data processingsystem either directly or through intervening I/O controllers.

In an embodiment, the input and the output devices may be implemented asa combined input/output device (illustrated in FIG. 9 with a dashed linesurrounding the input device 912 and the output device 914). An exampleof such a combined device is a touch sensitive display, also sometimesreferred to as a “touch screen display” or simply “touch screen”. Insuch an embodiment, input to the device may be provided by a movement ofa physical object, such as e.g. a stylus or a finger of a user, on ornear the touch screen display.

A network adapter 916 may also, optionally, be coupled to the dataprocessing system to enable it to become coupled to other systems,computer systems, remote network devices, and/or remote storage devicesthrough intervening private or public networks. The network adapter maycomprise a data receiver for receiving data that is transmitted by saidsystems, devices and/or networks to the data processing system 900, anda data transmitter for transmitting data from the data processing system900 to said systems, devices and/or networks. Modems, cable modems, andEthernet cards are examples of different types of network adapter thatmay be used with the data processing system 900.

SELECT EXAMPLES

Example 1 provides an apparatus for applying digital predistortion to aninput signal. The apparatus includes an actuator circuit, an adaptationcircuit, and an OOB regularization circuit. The actuator circuit isconfigured to use a model of a nonlinear electronic component to apply apredistortion to at least a portion of an input signal to generate anoutput of the actuator circuit (i.e., to predistort the input signalprior to providing it to the nonlinear electronic component), the inputsignal including a range of in-band (i.e., desired/target) frequencycomponents. The adaptation circuit is configured to update the modelbased on one or more captures of a feedback signal indicative of (e.g.,including, or being based on) an output of the nonlinear electroniccomponent, where capture includes L consecutive samples of the feedbacksignal, where L is an integer equal to or greater than 2. The OOBregularization circuit is configured to receive the output of theactuator circuit (where the output of the actuator circuit is the inputsignal to which the actuator circuit applied the predistortion), andgenerate an OOB error signal (ε_(oob)) indicative of OOB (i.e.,undesired) frequency components that might be present in the output ofthe actuator circuit and provide the OOB error signal to the adaptationcircuit. In turn, the adaptation circuit is configured to update themodel further based on the OOB error signal.

Example 2 provides the apparatus according to example 1, where the OOBregularization circuit includes a filter configured to filter the outputof the actuator circuit to generate the OOB error signal as a filteredoutput of the actuator circuit in which the in-band frequency componentsare attenuated (e.g., reduced or eliminated) and the OOB frequencycomponents are passed (e.g., maintained as they were without applyingany attenuation or amplification), amplified (e.g., gained in theirmagnitude), or attenuated by a smaller factor than that applied toattenuate the in-band frequency components. It might be suitable, insome implementations, to provide such a filter so that it would simplypass the OOB components, without any attenuation or amplification (i.e.,the factor by which the amplitude of these components is adjusted issubstantially 1.0). In case the filter is such that it gains the OOBcomponents (i.e., increases their amplitude), the factor by which theamplitude of these components is adjusted may be between about 1.0 and2.0, including all values and ranges therein, e.g., between about 1.0and 1.5, or between about 1.0. and 1.2. In case the filter is such thatit attenuates the OOB components (i.e., decreases their amplitude), thefactor by which the amplitude of these components is adjusted may bebetween about 0.5 and 1.0, including all values and ranges therein,e.g., between about 0.7 and 1.0, or between about 0.9 and 1.0. This maybe in contrast to the attenuation factor applied by the filter toattenuate the in-band components, where the attenuation factor may bebetween about 0 and 0.5, or between 0 and 0.2.

Example 3 provides the apparatus according to example 2, where thefilter is a high-pass filter.

Example 4 provides the apparatus according to any one of the precedingexamples, where the model includes a loss term that is based on a firstterm and a second term, the first term is indicative of a differencebetween the feedback signal (i.e., the output of the nonlinearcomponent) and the output of the actuator circuit, and the second termis indicative of an amount and/or a magnitude of the OOB frequencycomponents present in the output of the actuator circuit. In general,the second term may be a term that provides some measure of the DPDoutput that falls out of band, such as the power or mean square value.

Example 5 provides the apparatus according to example 4, where at leastone of the first term and the second term is a mean squared value.

Example 6 provides the apparatus according to examples 4 or 5, where theadaptation circuit updating the model includes the adaptation circuitupdating the model to decrease the loss function.

Example 7 provides the apparatus according to example 6, where theadaptation circuit updating the model to decrease the loss functionincludes the adaptation circuit implementing a Gauss-Newton algorithm todecrease the loss function. In other embodiments, other algorithms maybe used to decrease the loss function.

Example 8 provides the apparatus according to any one of the precedingexamples, where the adaptation circuit updating the model includes theadaptation circuit computing updated filter coefficients to be used inapplying the predistortion.

Example 9 provides the apparatus according to any one of the precedingexamples, where the adaptation circuit is configured to update the modelfurther based on a DPD error signal (ε_(dpd)) indicative of a differencebetween the output of the actuator circuit (i.e., a signal which may notonly include the in-band frequency components but also the OOB frequencycomponents) and the feedback signal (i.e., the output of the nonlinearcomponent).

Example 10 provides the apparatus according to any one of the precedingexamples, further including a PE regularization circuit configured toreceive the output of the actuator circuit (where the output of theactuator circuit is the input signal to which the actuator circuitapplied the predistortion), and generate a PE error signal (ε_(peak))indicative of samples that might be present in the output of theactuator circuit which have amplitude greater than a threshold, andprovide the PE error signal to the adaptation circuit, where theadaptation circuit is configured to update the model further based onthe PE error signal.

In various further embodiments according to example 10, the PEregularization circuit and the adaptation circuit may be configuredaccording to any one of examples 11-18.

Example 11 provides an apparatus for applying digital predistortion toan input signal. The apparatus includes an actuator circuit, anadaptation circuit, and a PE regularization circuit. The actuatorcircuit is configured to use a model of a nonlinear electronic componentto apply a predistortion to at least a portion of an input signal priorto generate an output of the actuator circuit (i.e., to predistort theinput signal prior to providing it to the nonlinear electroniccomponent). The adaptation circuit is configured to update the modelbased on one or more captures of a feedback signal indicative of (e.g.,including, or being based on) an output of the nonlinear electroniccomponent, where capture includes L consecutive samples of the feedbacksignal, where L is an integer equal to or greater than 2. The PEregularization circuit is configured to receive the output of theactuator circuit (where the output of the actuator circuit is the inputsignal to which the actuator circuit applied the predistortion), andgenerate a PE error signal (ε_(peak)) indicative of samples that mightbe present in the output of the actuator circuit which have an amplitudegreater than a threshold, and provide the PE error signal to theadaptation circuit, where the adaptation circuit is configured to updatethe model further based on the PE error signal.

Example 12 provides the apparatus according to example 11, where the PEregularization circuit includes a clipping circuit configured to clipthe amplitude of the samples in the output of the actuator circuit whichhave the amplitude greater than the threshold.

Example 13 provides the apparatus according to example 12, where the PEregularization circuit is configured to generate the PE error signalbased on a difference between the output of the actuator circuit and anoutput of the clipping circuit (i.e., the output of the actuator circuitin which the clipping circuit clipped the amplitude of the samples forthose samples that had the amplitude greater than the threshold).

Example 14 provides the apparatus according to any one of examples11-13, where the adaptation circuit is configured to update the modelfurther based on a DPD error signal (εdpd) indicative of a differencebetween the output of the actuator circuit (i.e., a signal which mayhave samples having amplitude greater than the threshold) and thefeedback signal (i.e., the output of the nonlinear component).

Example 15 provides the apparatus according to any one of examples11-14, where the model includes a loss term that is based on a firstterm and a second term, the first term is based on a DPD error signal(εdpd) indicative of a difference between the output of the actuatorcircuit (i.e., a signal which may have samples having amplitude greaterthan the threshold) and the feedback signal (i.e., the output of thenonlinear component), the second term is based on the PE error signal,and the adaptation circuit updating the model includes the adaptationcircuit updating the model to decrease the loss function. In general,the second term may be a term that provides some measure of the DPDoutput that has peak expansion, such as the power or mean square valuefor samples that had amplitude greater than a certain threshold.

Example 16 provides the apparatus according to example 15, where atleast one of the first term and the second term is a mean squared value.

Example 17 provides the apparatus according to examples 15 or 16, wherethe adaptation circuit updating the model to decrease the loss functionincludes the adaptation circuit implementing a Gauss-Newton algorithm todecrease the loss function. In other embodiments, other algorithms maybe used to decrease the loss function.

Example 18 provides the apparatus according to any one of examples11-17, where the adaptation circuit updating the model includes theadaptation circuit computing updated filter coefficients to be used inapplying the predistortion.

Example 19 provides an apparatus for applying digital predistortion toan input signal. The apparatus includes an actuator circuit, an errorcorrection circuit, and an adaptation circuit. The actuator circuit isconfigured to use a model of a nonlinear electronic component to apply apredistortion to at least a portion of an input signal to generate anoutput of the actuator circuit (i.e., to predistort the input signalprior to providing it to the nonlinear electronic component). The errorcorrection circuit is configured to receive the output of the actuatorcircuit (where the output of the actuator circuit is the input signal towhich the actuator circuit applied the predistortion), and generate anerror signal (e.g., ε_(oob) or ε_(peak)) indicative of a deviation ofthe output of the actuator circuit from a target/desired output. Theadaptation circuit is configured to update the model based on one ormore captures of a feedback signal indicative of (e.g., including, orbeing based on) an output of the nonlinear electronic component, wherecapture includes L consecutive samples of the feedback signal, where Lis an integer equal to or greater than 2, and further based on the errorsignal.

Example 20 provides the apparatus according to example 19, where themodel includes a loss term that is based on a first term and a secondterm, the first term is based on a DPD error signal (ε_(dpd)) indicativeof a difference between the output of the actuator circuit (i.e., asignal which may exhibit some undesirable behavior, e.g., a signal whichmay have samples having amplitude greater than the threshold, or asignal which may have frequency components outside of the desiredfrequency band) and the feedback signal (i.e., the output of thenonlinear component), the second term is based on the error signal, andthe adaptation circuit updating the model includes the adaptationcircuit updating the model to decrease the loss function.

Example 21 provides the apparatus according to example 20, where atleast one of the first term and the second term is weighted in the lossterm according to a weighting parameter.

Example 22 provides the apparatus according to examples 20 or 21, whereat least one of the first term and the second term is a mean squaredvalue.

Example 23 provides the apparatus according to any one of examples20-22, where the adaptation circuit updating the model to decrease theloss function includes the adaptation circuit implementing aGauss-Newton algorithm to decrease the loss function. In otherembodiments, other algorithms may be used to decrease the loss function.

Example 24 provides the apparatus according to any one of examples19-23, where the adaptation circuit is configured to update the modelfurther based on a DPD error signal (ε_(dpd)) indicative of a differencebetween the output of the actuator circuit (i.e., a signal which mayexhibit some undesirable behavior) and the feedback signal (i.e., theoutput of the nonlinear component).

Example 25 provides the apparatus according to any one of examples19-24, where the adaptation circuit updating the model includes theadaptation circuit computing updated filter coefficients to be used inapplying the predistortion.

Example 26 provides the apparatus according to any one of the precedingexamples, where the nonlinear electronic component is a power amplifier.

Example 27 provides a computer-implemented method of digitalpredistortion, the method including an actuator circuit using a model ofa nonlinear electronic component to apply a predistortion to at least aportion of an input signal to generate a predistorted output (i.e., topredistort the input signal prior to providing it to the nonlinearelectronic component); an error correction circuit generating an errorsignal (e.g., ε_(oob) or ε_(peak)) indicative of a deviation of thepredistorted output from a target/desired output; and an adaptationcircuit updating the model based on one or more captures of a feedbacksignal indicative of (e.g., including, or being based on) an output ofthe nonlinear electronic component, where capture includes L consecutivesamples of the feedback signal, where L is an integer equal to orgreater than 2, and further based on the error signal.

Example 28 provides the method according to example 27, where the inputsignal includes a range of in-band (i.e., desired/target) frequencycomponents, and the error signal is indicative of OOB (i.e., undesired)frequency components that might be present in the predistorted output.

Example 29 provides the method according to example 27, where the errorsignal is indicative of samples, which might be present in thepredistorted output, which have amplitude greater than a threshold.

Example 30 provides the method according to any one of examples 27-29,further including the adaptation circuit generating a DPD error signal(ε_(dpd)) indicative of a difference between the predistorted output andthe feedback signal, where the adaptation circuit updating the modelbased on the feedback signal includes the adaptation circuit updatingthe model based on the DPD error signal.

Example 31 provides the method according to example 30, where the modelincludes a loss term that is based on a first term and a second term,the first term is based on the DPD error signal, the second term isbased on the error signal, and the adaptation circuit updating the modelincludes the adaptation circuit updating the model to decrease the lossfunction.

Example 32 provides the method according to example 31, where at leastone of the first term and the second term is a mean squared value.

Example 33 provides the method according to examples 31 or 32, where theadaptation circuit updating the model to decrease the loss functionincludes the adaptation circuit implementing a Gauss-Newton algorithm todecrease the loss function. In other embodiments, other algorithms maybe used to decrease the loss function.

Example 34 provides the method according to any one of examples 27-33,where the adaptation circuit updating the model includes the adaptationcircuit computing updated filter coefficients to be used in applying thepredistortion.

Example 35 provides the method according to any one of examples 27-34,where the nonlinear electronic component is a power amplifier.

Example 36 provides a non-transitory computer-readable storage mediumincluding instructions for execution which, when executed by aprocessor, are operable to perform operations of a method according toany one of the preceding examples (e.g., the method according to any oneof examples 27-35), and/or operations to enable performing DPD in anapparatus according to any one of the preceding examples (e.g., theapparatus according to any one of examples 1-26). Thus, in someexamples, the non-transitory computer-readable storage medium accordingto example 36 may further include instructions operable to performoperations performed by any parts of the communication system inaccordance with any one of the preceding examples.

Variations and Implementations

While embodiments of the present disclosure were described above withreferences to exemplary implementations as shown in FIGS. 1-9, a personskilled in the art will realize that the various teachings describedabove are applicable to a large variety of other implementations.

In certain contexts, the features discussed herein can be applicable toautomotive systems, safety-critical industrial applications, medicalsystems, scientific instrumentation, wireless and wired communications,radio, radar, industrial process control, audio and video equipment,current sensing, instrumentation (which can be highly precise), andother digital-processing-based systems.

In the discussions of the embodiments above, components of a system,such as filters, converters, mixers, and/or other components can readilybe replaced, substituted, or otherwise modified in order to accommodateparticular circuitry needs. Moreover, it should be noted that the use ofcomplementary electronic devices, hardware, software, etc., offer anequally viable option for implementing the teachings of the presentdisclosure related to DPD with OOB and/or PE regularization, or DPDusing any error signal based on the output of a DPD actuator circuit, invarious communication systems.

Parts of various systems for implementing DPD with OOB and/or PEregularization, or DPD using any error signal based on the output of aDPD actuator circuit, as proposed herein can include electroniccircuitry to perform the functions described herein. In some cases, oneor more parts of the system can be provided by a processor speciallyconfigured for carrying out the functions described herein. Forinstance, the processor may include one or more application specificcomponents, or may include programmable logic gates which are configuredto carry out the functions describe herein. The circuitry can operate inanalog domain, digital domain, or in a mixed-signal domain. In someinstances, the processor may be configured to carrying out the functionsdescribed herein by executing one or more instructions stored on anon-transitory computer-readable storage medium.

In one example embodiment, any number of electrical circuits of thepresent figures may be implemented on a board of an associatedelectronic device. The board can be a general circuit board that canhold various components of the internal electronic system of theelectronic device and, further, provide connectors for otherperipherals. More specifically, the board can provide the electricalconnections by which the other components of the system can communicateelectrically. Any suitable processors (inclusive of DSPs,microprocessors, supporting chipsets, etc.), computer-readablenon-transitory memory elements, etc. can be suitably coupled to theboard based on particular configuration needs, processing demands,computer designs, etc. Other components such as external storage,additional sensors, controllers for audio/video display, and peripheraldevices may be attached to the board as plug-in cards, via cables, orintegrated into the board itself. In various embodiments, thefunctionalities described herein may be implemented in emulation form assoftware or firmware running within one or more configurable (e.g.,programmable) elements arranged in a structure that supports thesefunctions. The software or firmware providing the emulation may beprovided on non-transitory computer-readable storage medium comprisinginstructions to allow a processor to carry out those functionalities.

In another example embodiment, the electrical circuits of the presentfigures may be implemented as stand-alone modules (e.g., a device withassociated components and circuitry configured to perform a specificapplication or function) or implemented as plug-in modules intoapplication specific hardware of electronic devices. Note thatparticular embodiments of the present disclosure may be readily includedin a system on chip (SOC) package, either in part, or in whole. An SOCrepresents an IC that integrates components of a computer or otherelectronic system into a single chip. It may contain digital, analog,mixed-signal, and often RF functions: all of which may be provided on asingle chip substrate. Other embodiments may include a multi-chip-module(MCM), with a plurality of separate ICs located within a singleelectronic package and configured to interact closely with each otherthrough the electronic package.

It is also imperative to note that all of the specifications,dimensions, and relationships outlined herein (e.g., the number ofcomponents of the communication system shown in FIGS. 1, 5, and 6) haveonly been offered for purposes of example and teaching only. Suchinformation may be varied considerably without departing from the spiritof the present disclosure, or the scope of the appended claims. Itshould be appreciated that the system can be consolidated in anysuitable manner. Along similar design alternatives, any of theillustrated circuits, components, modules, and elements of the presentfigures may be combined in various possible configurations, all of whichare clearly within the broad scope of this specification. In theforegoing description, example embodiments have been described withreference to particular processor and/or component arrangements. Variousmodifications and changes may be made to such embodiments withoutdeparting from the scope of the appended claims. The description anddrawings are, accordingly, to be regarded in an illustrative rather thanin a restrictive sense.

It is also important to note that the functions related to DPD with OOBand/or PE regularization, or DPD using any error signal based on theoutput of a DPD actuator circuit, as proposed herein illustrate onlysome of the possible functions that may be executed by, or within,communication systems. Some of these operations may be deleted orremoved where appropriate, or these operations may be modified orchanged considerably without departing from the scope of the presentdisclosure. Substantial flexibility is provided by embodiments describedherein in that any suitable arrangements, chronologies, configurations,and timing mechanisms may be provided without departing from theteachings of the present disclosure.

The invention claimed is:
 1. An apparatus for applying digitalpredistortion to an input signal, the apparatus comprising: an actuatorcircuit, to use a model of a nonlinear electronic component to apply apredistortion to at least a portion of an input signal to generate anoutput of the actuator circuit; an adaptation circuit, to update themodel based on a feedback signal indicative of an output of thenonlinear electronic component; and a peak expansion (PE) regularizationcircuit, to: receive the output of the actuator circuit, and generate aPE error signal based on differences between amplitudes of samples inthe output of the actuator circuit and a threshold, wherein: fordifferent samples of the samples in the output of the actuator circuit,the PE error signal is indicative of the differences determined withrespect to a single threshold value of the threshold, the model includesa loss function that is indicative of a sum of a first term and a secondterm, the first term is indicative of a difference between the feedbacksignal and the output of the actuator circuit, the second term isindicative of the PE error signal, and the adaptation circuit is toupdate the model further based on the PE error signal in a way thatdecreases the loss function.
 2. The apparatus according to claim 1,wherein the PE regularization circuit includes a clipping circuit toclip the amplitude of the samples in the output of the actuator circuitwhich have the amplitudes greater than the threshold.
 3. The apparatusaccording to claim 2, wherein the PE regularization circuit is togenerate the PE error signal based on a difference between the output ofthe actuator circuit and an output of the clipping circuit.
 4. Theapparatus according to claim 1, wherein the adaptation circuit is toupdate the model further based on a DPD error signal indicative of adifference between the output of the actuator circuit and the feedbacksignal.
 5. The apparatus according to claim 1, wherein at least one ofthe first term and the second term is a mean squared value.
 6. Theapparatus according to claim 1, wherein at least one of the first termand the second term is weighted in the loss function according to aweighting parameter.
 7. The apparatus according to claim 1, wherein theadaptation circuit is to compute updated coefficients as {circumflexover (θ)}_(k)={circumflex over(θ)}_(k−1)+μ{Y^(H)Y+λZ^(H)Z}⁻¹{Y^(H)ε_(dpd)+λZ^(H)ε_(peak)}, where{circumflex over (θ)}_(k) are the updated coefficients of the model forthe next iteration, {circumflex over (θ)}_(k−1) are coefficients of themodel for a previous iteration, Y is a gradient of the first term of theloss function, Z is a gradient of the second term of the loss function,and X is a basis matrix of digital predistortion features.
 8. Theapparatus according to claim 1, further comprising an out-of-band (OOB)regularization circuit to: receive the output of the actuator circuit,and generate an OOB error signal indicative of OOB frequency componentsin the output of the actuator circuit, wherein the adaptation circuit isto update the model further based on the OOB error signal.
 9. Theapparatus according to claim 8, wherein the OOB regularization circuitincludes an OOB filter to filter the output of the actuator circuit tobe provided to the nonlinear electronic component to generate the OOBerror signal as a filtered output of the actuator circuit in which thein-band frequency components are attenuated and the OOB frequencycomponents are passed, amplified, or attenuated by a smaller factor thanthat applied to attenuate the in-band frequency components.
 10. A radiofrequency (RF) communication system, comprising: a transmitter circuit,comprising a nonlinear electronic component to generate an output; areceiver circuit to receive a feedback signal indicative of the outputof the nonlinear electronic component; and a digital predistortion (DPD)circuit to: use a model of the nonlinear electronic component to apply apredistortion to at least a portion of the input signal to generate apredistorted input signal, where the nonlinear electronic component isto generate the output based on the predistorted input signal; generatea peak expansion (PE) error signal indicative of a plurality of samplesof the predistorted input signal having amplitudes greater than athreshold, wherein the threshold to which the amplitudes of theplurality of samples are compared to in order to generate the PE errorsignal is a same threshold; and update the model based on the feedbacksignal and the PE error signal, wherein: the model includes a lossfunction that is indicative of a sum of a first term and a second term,the first term is indicative of a difference between the feedback signaland the predistorted input signal, and the second term is indicative ofthe PE error signal.
 11. The RF communication system according to claim10, wherein the nonlinear electronic component is a power amplifier andthe RF communication system includes the power amplifier.
 12. Anapparatus for applying digital predistortion to an input signal, theapparatus comprising: an actuator circuit, to use a model of a nonlinearelectronic component to apply a predistortion to at least a portion ofan input signal to generate an output of the actuator circuit; anadaptation circuit, to update the model based on a feedback signalindicative of an output of the nonlinear electronic component; and apeak expansion (PE) regularization circuit to: receive the output of theactuator circuit, and generate a PE error signal indicative of samplesin the output of the actuator circuit which have an amplitude greaterthan a fixed threshold, wherein: the model includes a loss function thatis indicative of a sum of a first term and a second term, the first termis indicative of a difference between the feedback signal and the outputof the actuator circuit, the second term is indicative of the PE errorsignal, and the adaptation circuit is to update the model further basedon the PE error signal in a way that decreases the loss function. 13.The apparatus according to claim 12, wherein at least one of the firstterm and the second term is a mean squared value.
 14. The apparatusaccording to claim 12, wherein at least one of the first term and thesecond term is weighted in the loss function according to a weightingparameter.
 15. The apparatus according to claim 12, further comprisingan out-of-band (OOB) regularization circuit to: receive the output ofthe actuator circuit, and generate an OOB error signal indicative of OOBfrequency components in the output of the actuator circuit, wherein theadaptation circuit is to update the model further based on the OOB errorsignal.
 16. The apparatus acccording to claim 15, wherein the OOBregularization circuit includes an OOB filter to filter the output ofthe actuator circuit to be provided to the nonlinear electroniccomponent to generate the OOB error signal as a filtered output of theactuator circuit in which the in-band frequency components areattenuated and the OOB frequency components are passed, amplified, orattenuated by a smaller factor than that applied to attenuate thein-band frequency components.
 17. The apparatus according to claim 12,wherein the apparatus includes a radio frequency (RF) transmitter and anRF receiver.
 18. The apparatus according to claim 12, wherein thenonlinear electronic component is a power amplifier.
 19. The apparatusaccording to claim 18, wherein the apparatus includes the poweramplifier.
 20. The apparatus according to claim 19, wherein theapparatus is a radio frequency device.